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A074871
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Start with n and repeatedly apply the map k -> T(k) = A053837(k) + A171765(k); a(n) is the number of steps (at least one) until a prime is reached, or 0 if no prime is ever reached.
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2
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0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 0, 1, 2, 2, 0, 1, 3, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 0, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 0, 1, 1, 2, 3, 1, 2, 1, 1, 0, 1, 1, 0, 1, 0
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OFFSET
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1,17
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COMMENTS
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The first occurrence of k beginning with 0: 1, 2, 17, 59, 337, 779, 16999, 6888888, ..., . - Robert G. Wilson v, Oct 20 2010
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LINKS
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EXAMPLE
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T(2)=2. So in one step we reach a prime.
T(3)=3 and then in one step again we reach a prime.
T(4)=4 and we will never reach a prime.
T(11)=1+2=3 and again in one step we reach a prime.
T(17)=7+8=15 --> T(15)=5+6=11 and then in two steps we reach a prime.
T(13)=3+4=7 and then 1 step......
T(14)=4+5=9 --> T(9)=9 --> T(9)=9........ and we will never reach a prime.
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MATHEMATICA
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g[n_] := Block[{id = IntegerDigits@ n}, Mod[ Plus @@ id, 10] + If[n < 10, 0, Times @@ id]]; f[n_] := Block[{lst = Rest@ NestWhileList[g, n, UnsameQ, All]}, lsp = PrimeQ@ lst; If[ Last@ Union@ lsp == False, 0, Position[lsp, True, 1, 1][[1, 1]]]]; Array[f, 105] (* Robert G. Wilson v, Oct 20 2010 *)
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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